astronomy
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CopyofOrbits-Kepler2.docx
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Recorder: Mole: .
Kepler’s Second Law
Kepler’s second law of planetary motion:
A line joining a planet and its Sun sweeps out equal amounts of area in equal amounts of time.
Here is a planet moving in a perfectly circular orbit around its star. The time between each position is exactly 1 month.
A
B
C
D
E
F
G
H
I
J
K
L
1. Does this planet obey Kepler’s second law? Explain how.
2. Is this planet’s speed increasing, decreasing, or staying the same throughout its orbit? Explain.
The next diagram shows a planet that obeys Kepler’s second law.
C
D
E
F
G
H
I
A
B
3. Draw two lines:
a. Draw a line connecting the position A to the star.
b. Draw a line connecting position B to the star
c. Fill in the area between the lines: the area swept out by the planet as it travels from position A to position B.
4. Using positions C-I, choose a pair of positions that sweep out the same full area triangle as you shaded in question 3.
a. (No calculations needed. Eyeball it. You may assume that if a distance looks identical, it is identical)
5. Is the time it takes for the planet to travel from position A to B greater than, less than, or equal to the time it takes the planet to travel between the two positions in question 4. Explain why. Use Kepler’s second law.
6. Is the distance that the planet travels from position A to B greater than, less than, or equal to the distance it travels between the two positions in question 4? Explain why. Use Kepler’s second law.
7. During which interval will the planet be travelling faster? A to B, or the two positions in question 4?
The next diagram shows a planet that obeys Kepler’s second law.
The positions marked are exactly one month apart.
C
D
E
F
G
H
I
A
B
J
K
L
8. Does the planet travel the same distance each month?
9. Where is the planet travelling the fastest?
10. Where is the planet travelling the slowest?
11. At position K, is the planet speeding up or slowing down? Explain.
12. Describe, in one sentence the relationship between the planets speed and its distance from its star.
An orbit with an eccentricity of 0 is a perfect circle.
The highly elliptical orbits you saw on previous pages would have an eccentricity of approximately 0.90.
Object |
Orbital Eccentricity |
|
Examples of ellipses and their eccentricities (e) |
|
Mercury |
0.206 |
|
http://astro.wsu.edu/worthey/astro/html/lec-ellipse.html |
|
Venus |
0.007 |
|
|
|
Earth |
0.016 |
|
|
|
Mars |
0.093 |
|
|
|
Jupiter |
0.048 |
|
|
|
Saturn |
0.054 |
|
|
|
Uranus |
0.047 |
|
|
|
Neptune |
0.008 |
|
|
|
Pluto |
0.248 |
|
|
13. Which of these orbits most closely matches the shape of the Earth’s orbit around the Sun? Why
A.
B.
C.
14. Which object orbiting the Sun in the table would experience the biggest change in speed? The smallest?
15. How much does Earth’s speed around the Sun change throughout the year? Use the answer to question 13, the table, and Kepler’s second law in your answer. Explain:
